you guys are the best. most students never get it because everything is pre-packaged in an axiomatic construction. the history of how it came about is more instructive than the cleaned up abbreviated version of the axiomatic method. when people don't know the inspiration for how a thing came about, it is much harder to understand and extend.

Going from an intuitive algebraic problem to a general geometric one is very powerful

congrats on on 100K subscribers

Somehow, I constantly waited for an introduction to multivectors. So powerful if you get acquainted to them: You can check solvability in one product. If n vectors give a zero product, you know they are not independent.

You always manage to make videos about my favorite topics!

FIRST!!! Big love to you guys for making this videos!!!!:face-red-heart-shape:

Awesome video, looking forward to the next one!

Thanks man, been stuck in couple days try to find a better word for addition when working with scaling displacement vector and you just beautifully show it att 3.10 - 3.13

Nice content 👌👌 really liked linear algebra, one of the best classes in university

Congratulations Sir and Maam for the amazing fest of subscribers... Good wishes for the future...

Ur videos are soooo funnn to watch and understand

You are fun and your minds are in a very cool place when you see my post but this takes time because as simultaneously happens I have other proofs to answer other questions just like what you say here but the difference is it is brand new but it is old and has been created years ago.😊

Nice explaination

Loved the content, keep it coming!

You explained this so well, thank you!

Thanks for sharing this, learned a lot.

Cool very cool totally understand this displacements where things are different but line up at one point or the other and my friend is where my system is built because I know they line up and yes make a question knowing the answers but hold back on the key and say and know what that calculations is before I figured out yes my friend this is one of my favorite ways to even trick the numbers that will not be tricked.😊

Congratulations! Blessings

I have a suggestion. Stick with one speaker throughout one video. When you switch from one to the other it distracts my brain. You can have both conversing with each other or just one speaker throughout the video. You can switch between videos.

You might ask "What about n points in multidimensional space?". In the video, you mentioned three vectors and asked if they were degenerate or formed the 3D space. But those three vectors thought of as point forms a k-simplex. So you might ask "Does these k points form an n-simplex?". Then lead to algebraic geometry and generalized Stoke's Theorem as a way to learn all the concepts from Vector Calculus. Points are 0-simplex. Lines are 1-simplex. Triangles are 2-simplices. Tetrahedrons are 3-simplices. Omit one point of an n-simplex and call it a face of that n-simplex. Form the boundary to the n-simplex. Mention k-forms and how generalized Stoke's theorem looks very simple but it explains all of Calculus 3 (Vector Calculus). You might have created a video of this but I do not recall if you mentioned generalized Stoke's Theorem which is ultra cool. Relate to Maxwell's Equations which to d(F) and d(*F) or something like that.